A block accelerates at 3.4 m/s^2 down a plane
inclined at an angle 26.0◦
Find µk between the block and the inclined plane. The acceleration of gravity is 9.81 m/s^2
.
1. 0.0323689
2. 0.162268
3. 0.177148
4. 0.0976626
5. 0.102121
6. 0.13473
7. 0.113463
8. 0.224231
9. 0.185358
10. 0.0613983
Thanks
The friction-free acceleration would be
9.81 sin26° = 4.3
so µk = 3.4/4.3
To find the coefficient of kinetic friction (μk) between the block and the inclined plane, we can use the following equation:
μk = tan(θ) - (a/g)
where θ is the angle of the inclined plane, a is the acceleration of the block down the inclined plane, and g is the acceleration due to gravity.
Given:
θ = 26.0°
a = 3.4 m/s^2
g = 9.81 m/s^2
Substituting the given values into the equation, we get:
μk = tan(26.0°) - (3.4/9.81)
Calculating this expression:
μk = 0.4877 - 0.3466
μk ≈ 0.1411
So, the coefficient of kinetic friction (μk) between the block and the inclined plane is approximately 0.1411.
None of the given answer options matches this result.
To find the coefficient of kinetic friction (μk) between the block and the inclined plane, we can use the following equation:
μk = tan(θ) - (a/g)
Where:
θ = angle of the inclined plane = 26.0 degrees
a = acceleration of the block down the inclined plane = 3.4 m/s^2
g = acceleration due to gravity = 9.81 m/s^2
Substituting the given values into the equation, we have:
μk = tan(26.0°) - (3.4 m/s^2 / 9.81 m/s^2)
Using a scientific calculator, we can find the value of tan(26.0°) which is approximately 0.4877. Substituting this value and the given values, we can calculate μk:
μk = 0.4877 - (3.4 m/s^2 / 9.81 m/s^2)
μk ≈ 0.4877 - 0.3463
μk ≈ 0.1414
Round the value to the appropriate number of significant figures, we get:
μk ≈ 0.141
None of the provided answer options match this value exactly. However, the closest option is 0.13473, which rounds to 0.135 when rounded to three decimal places.
Therefore, the closest option to the coefficient of kinetic friction (μk) between the block and the inclined plane is 0.13473.